Two women who have been a couple for 32 years were among the first to be granted a same-sex marriage licence in Washington state early on Thursday morning.

A law legalising same-sex unions took effect at midnight, and officials geared up for a flood of applications from gay and lesbian couples eager to exchange vows.

In Olympia, the state capital, the Thurston County auditor's office planned to grant marriage licenses to the 15 same-sex couples who entered a lottery to be served first at midnight.

Lisa Brodoff and Lynn Grotsky, partners of nearly 32 years, became the first same-sex couple in Thurston County, and likely the state, to receive a marriage license, to the cheers of a crowd of other same-sex couples and supporters.

"We have the greatest feeling of happiness and relief and excitement," said Brodoff, 57, a law professor at Seattle University.

Grotsky, a 56-year-old social worker, told Reuters that when she and Brodoff became a couple, they were afraid to tell acquaintances and co-workers that they were lesbians. "Everything was a fight and a conflict," Grotsky said. "Now it's like we're regular people."

Washington made history last month as one of three US states where marriage rights were extended to same-sex couples by popular vote, joining Maryland and Maine in passing ballot initiatives on 6 November recognising gay unions.

Washington became the first of those states to put its law into effect – it became law at the stroke of midnight – and same-sex marriage is set to go on the books in Maine on 29 December and in Maryland on 1 January.

Under Washington state law, all couples must get their marriage certificates at least three days in advance. So the first wave of same-sex Washington weddings – expected to number in the hundreds – is scheduled for Sunday.

In Seattle, about 150 same-sex couples lined up outside county offices shortly before midnight, waiting in a festive atmosphere for the doors to open to obtain marriage licenses. Some sat in lawn chairs and others brought late-night picnics.

The Democratic-controlled state legislature in Washington passed a bill to legalise gay marriage in February, and Democratic governor Christine Gregoire swiftly signed it into law.

But opponents collected enough signatures to temporarily block the measure from taking effect and force the issue onto the state ballot in November. Voters passed it by 54% to 46%.

"It feels like we're on even ground," said Derek Hoffman, 33, who received a license in Olympia to marry his partner of 10 years, Chris Waterman, 35. "Like not being less than other people."

Olympia residents Tina Roose and Teresa Guajardo said they would wait until 15 December to marry, having reserved the majestic state capitol rotunda for a pre-Christmas wedding ceremony.

The uncertainty of the ballot initiative process proved a bit of a nail-biter as Roose and Guajardo waited for the election results to see if they could keep their reservation. "I am able to marry the person that I love," Roose said. She said the couple had invited others, both gay and straight, to tie the knot alongside them at the capitol.

"I just ran into a colleague today at a grocery," added Roose, a retired librarian. "She was so excited. She asked all the typical questions like: 'What are you going to wear?'"

As for those who voted against same-sex marriage, Roose said she hoped they would be won over "with love".

"You can only change people's attitudes one heart at a time," she said.